When should a word be singular and when should it be in plural when it comes to generality?

They should usually be plural. "Man" is an exception.

If you say "The man is explicable by..." it means we were talking about a specific man, and that he is explicable by nothing less than all his history.

You should say:

Men are explicable by nothing less than all their history.

because you want to use plural when referring to a generality. However, Man has another definition:

The human race: humankind

"Man" is frequently used as a metaphor for all of humankind, which is why you can use 'man' to refer to a generality. You could just as easily say

Humankind is explicable by nothing less than all it's history.

Will it be ok if I use singular in the sentence above instead:

Word is the foundation of a language.

No, this is incorrect. The reason you can use 'man' is because of this second definition. "Word" does not have a second definition meaning "All words". Although, you could say:

Speech is the foundation of a language.